The skepticism is very understandable. It is important to scrutinise solutions like this to make sure that they indeed do as they say they do, and to make sure the government doesn't overreach with their authority.
That said, it should also be possible for laws to be enforced, and there are laws on the books that are supposed to prevent children from accessing things that we as a society have agreed they have no business accessing (alcohol, tabacco, porn, and increasingly commonly social media)
Currently there is no good method to actually enforce those laws on the internet, so there needs to be a solution for that.
I think this form of age verification may be a decent compromise between privacy and the need to enforce these existing laws.
Edit: Typo. I wrote "they" instead of "that"